Not sure how to properly update persistent JPA entities

Let's say I have a Category entity that contains a list of Product entities which fall under that category:

Category c = new Category(/*some JSON with category attributes*/);

The Category entity is persisted using this CategoryManager:

// imports

@RequestScoped
public class CategoryManager {
    @PersistenceContext
    private EntityManager em;

    public CategoryManager() {}

    @Transactional
    public void save(Category c) {
        em.persist(c);
    }

    public Category find(long id) {
        return em.find(Category.class, id);
    }

    // other methods
}

Now there's a function that is supposed to create a new Product entity and add it into the list of products of a certain category:

@POST
@Consumes(MediaType.APPLICATION_JSON)
@Produces(MediaType.APPLICATION_JSON)
public Response addProduct(ProductDTO product) {
    Category category = categoryManager.find(product.getCategory().getId());

    if (category == null)
        return Response.status(Response.Status.NOT_FOUND).entity("Category not found.").build();

    Product new_product = new Product(product);
    productManager.save(new_product);
    category.getProducts().add(new_product);
    // categoryManager.save(category);

    return Response.ok(new_product).build();
}

This seems to update the database correctly, but when I try to list the category, its list of products appears empty in JSON:

{
    "id": 1,
    "name": "Bread",
    "products": []
}

Only after I restart my Open Liberty server does it actually list the products correctly:

{
    "id": 1,
    "name": "Bread",
    "products": [
        {
            "id": 2,
            "name": "Wholegrain"
        }
    ]
}

I suspect it's because I don't save the category after appending the product to its list of products, but when I uncomment the commented out line in the code I posted, it complains about duplicate key values.

So I ended up fixing this by adding the following to my CategoryManager:

@Transactional
public Category update(Category c) {
    return em.merge(c);
}

And updating the addProduct() method like this:

@POST
@Consumes(MediaType.APPLICATION_JSON)
@Produces(MediaType.APPLICATION_JSON)
public Response addProduct(ProductDTO product) {
    Category category = categoryManager.find(product.getCategory().getId());

    if (category == null)
        return Response.status(Response.Status.NOT_FOUND).entity("Category not found.").build();

    Product new_product = new Product(product);
    productManager.save(new_product);
    category.getProducts().add(new_product);
    categoryManager.update(category); // <---- the changed line

    return Response.ok(new_product).build();
}

It seems to have fixed the issue, but I'm open to suggestions and better solutions.